Geodesic
Integrability and stochastic behavior in some nonholonomic dynamics problems
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 257-265

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In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of an ellipsoid on a plane and a sphere. We research these problems using Poincaré maps, which investigation helps to discover a new integrable case.
Keywords: nonholonomic constraint, invariant measure, first integral, Poincaré map, integrability and chaos. 
@article{ND_2013_9_2_a4,
     author = {Ivan A. Bizyaev and Alexey O. Kazakov},
     title = {Integrability and stochastic behavior in some nonholonomic dynamics problems},
     journal = {Russian journal of nonlinear dynamics},
     pages = {257--265},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_2_a4/}
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Ivan A. Bizyaev; Alexey O. Kazakov. Integrability and stochastic behavior in some nonholonomic dynamics problems. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 257-265. http://geodesic.mathdoc.fr/item/ND_2013_9_2_a4/